Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class C816 {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int h = sc.nextInt();
		int w = sc.nextInt();
		int sAll = 0;
		int sCount = 0;
		int[][] g = new int[w][h];
		for (int i = 0; i < h; i++) {
			for (int j = 0; j < w; j++) {
				g[j][i] = sc.nextInt();
				sAll += g[j][i];
			}
		}

		StringBuilder ans = new StringBuilder();
		int nAns = 0;
		
		if (h > w) {
			for (int x = 0; x < w; x++) {
				int min = Integer.MAX_VALUE;
				int dec = 0;
				for (int y = 0; y < h; y++) {
					min = min<g[x][y] ? min : g[x][y];
				}
				for (int i = 0; i < min; i++) {
					ans.append("col " + (x+1) + "\n");
					sCount += h;
					nAns++;
					dec++;
				}
				if (dec > 0) {
					for (int y = 0; y < h; y++) {
						g[x][y] -= dec;
					}
				}
			}
		}
		
		for (int y = 0; y < h; y++) {
			int min = Integer.MAX_VALUE;
			int dec = 0;
			for (int x = 0; x < w; x++) {
				min = min<g[x][y] ? min : g[x][y];
			}
			for (int i = 0; i < min; i++) {
				ans.append("row " + (y+1) + "\n");
				sCount += w;
				nAns++;
				dec++;
			}
			if (dec > 0) {
				for (int x = 0; x < w; x++) {
					g[x][y] -= dec;
				}
			}
		}
		
		if (w >= h) {
			for (int x = 0; x < w; x++) {
				int min = Integer.MAX_VALUE;
				for (int y = 0; y < h; y++) {
					min = min<g[x][y] ? min : g[x][y];
				}
				for (int i = 0; i < min; i++) {
					ans.append("col " + (x+1) + "\n");
					sCount += h;
					nAns++;
				}
			}
		}
		
		System.out.println(sCount == sAll ? nAns + "\n" + ans.toString() : -1);
	}
}